Question

10 Brief E 14-2 Determining the price of bonds [LO14-2) (Use a factor(s) from the tables provided. Enter your answers in whole dollars. Round final answers to the nearest whole

Answer 1

Answer- when the market rate differs from bond's stated rate, the bond will sell either at a higher or lower than face value. The price of a bond can be calculated using the market rate,coupon rate, no. of payments and face value of the bonds.

n= 40 (20 years*2 payments per year)

i= 3.00% (6%/2 payments per year)

Step 1: Formula: c * F * ((1 - (1 + m)^-t ) / m)

m = market rate 3.0% (6% / 2 because of semi-annual payments)

c = bond rate 2.5% (5% / 2 because of semi-annual payments)

t = # of periods 40 (20 years * 2 because of semi-annual payments)

F = face amount 80,000,000

2.5% * 80,000,000 * ((1 - (1 + 3.0%)^-40) / 3.0% = 46,229,544

Step 2: Because of semi-annual payments, divide the market rate by 2 and multiply the # of payments by 2.

Formula: F / ((1 + m)^t )

80,000,000 / ((1 + 3.0%)^40) = 24,524,547

Step 3:

Add steps 1 & 2 together to get the price of the bond:

$46,229,544	Present value of interest payments
$24,524,547	Present value of the face amount of the bond
$70,754,091	Price of the bond